Abstract Sediment transport by wind or water near the threshold of grain motion is dominated by rare transport events. This intermittency makes it difficult to calibrate sediment transport laws, or to define an unambiguous threshold for grain entrainment, both of which are crucial for predicting sediment transport rates. We present a model that captures this intermittency and shows that the noisy statistics of sediment transport contain useful information about the sediment entrainment threshold and the variations in driving fluid stress. Using a combination of laboratory experiments and analytical results, we measure the threshold for grain entrainment in a novel way and introduce a new property, the “shear stress variability”, which predicts conditions under which transport will be intermittent. Our work suggests strategies for improving measurements and predictions of sediment flux and hints that the sediment transport law may change close to the threshold of motion.
The following note shows that the symmetry of various resistance formulae, often based on Lorentz reciprocity for linearly viscous fluids, applies to a wide class of nonlinear viscoplastic fluids. This follows from Edelen's nonlinear generalization of the Onsager relation for the special case of strongly dissipative rheology, where constitutive equations are derivable from his dissipation potential. For flow domains with strong dissipation in the interior and on a portion of the boundary, this implies strong dissipation on the remaining portion of the boundary, with strongly dissipative traction-velocity response given by a dissipation potential. This leads to a nonlinear generalization of Stokes resistance formulae for a wide class of viscoplastic fluid problems. We consider the application to nonlinear Darcy flow and to the effective slip for viscoplastic flow over textured surfaces.
Fine-particle suspensions (such as cornstarch mixed with water) exhibit dramatic changes in viscosity when sheared, producing fascinating behaviors that captivate children and rheologists alike. Examination of these mixtures in simple flow geometries suggests intergranular repulsion and its influence on the frictional nature of granular contacts is central to this effect-for mixtures at rest or shearing slowly, repulsion prevents frictional contacts from forming between particles, whereas when sheared more forcefully, granular stresses overcome the repulsion allowing particles to interact frictionally and form microscopic structures that resist flow. Previous constitutive studies of these mixtures have focused on particular cases, typically limited to 2D, steady, simple shearing flows. In this work, we introduce a predictive and general, 3D continuum model for this material, using mixture theory to couple the fluid and particle phases. Playing a central role in the model, we introduce a microstructural state variable, whose evolution is deduced from small-scale physical arguments and checked with existing data. Our space- and time-dependent model is implemented numerically in a variety of unsteady, nonuniform flow configurations where it is shown to accurately capture a variety of key behaviors: 1) the continuous shear-thickening (CST) and discontinuous shear-thickening (DST) behavior observed in steady flows, 2) the time-dependent propagation of "shear jamming fronts," 3) the time-dependent propagation of "impact-activated jamming fronts," and 4) the non-Newtonian, "running on oobleck" effect, wherein fast locomotors stay afloat while slow ones sink.
Data from DEM-LBM simulations of round sediment particles and continuum models:-single_sphere: single sphere tests of DEM-LBM for validation-flume: DEM-LBM flume tests, compared with the corresponding experiments-wide_wall_free: DEM-LBM simulations, wide wall free cases-continuum: continuum modeling results-fluid_bc: pure fluid LBM tests to validate the boundary condition for the flume tests
data/: Data from DEM-LBM simulations of round sediment particles and continuum models -single_sphere: single sphere tests of DEM-LBM for validation -flume: DEM-LBM flume tests, compared with the corresponding experiments -wide_wall_free: DEM-LBM simulations, wide wall free cases -continuum: continuum modeling results -fluid_bc: pure fluid LBM tests to validate the boundary condition for the flume tests make_figures/: The figures can be generated using the Matlab files Code/: The programs used to get the DEM-LBM results and continuum modeling results are available
data/: Data from DEM-LBM simulations of round sediment particles and continuum models -single_sphere: single sphere tests of DEM-LBM for validation -flume: DEM-LBM flume tests, compared with the corresponding experiments -wide_wall_free: DEM-LBM simulations, wide wall free cases -continuum: continuum modeling results -fluid_bc: pure fluid LBM tests to validate the boundary condition for the flume tests make_figures/: The figures can be generated using the Matlab files Code/: The programs used to get the DEM-LBM results and continuum modeling results are available
Data from DEM-LBM simulations of round sediment particles and continuum models:-single_sphere: single sphere tests of DEM-LBM for validation-flume: DEM-LBM flume tests, compared with the corresponding experiments-wide_wall_free: DEM-LBM simulations, wide wall free cases-continuum: continuum modeling results-fluid_bc: pure fluid LBM tests to validate the boundary condition for the flume tests
Generalizing Maxwell's (Maxwell 1867 IV. Phil. Trans. R. Soc. Lond.157, 49-88 (doi:10.1098/rstl.1867.0004)) classical formula, this paper shows how the dissipation potentials for a dissipative system can be derived from the elastic potential of an elastic system undergoing continual failure and recovery. Hence, stored elastic energy gives way to dissipated elastic energy. This continuum-level response is attributed broadly to dissipative microscopic transitions over a multi-well potential energy landscape of a type studied in several previous works, dating from Prandtl's (Prandtl 1928 Ein Gedankenmodell zur kinetischen Theorie der festen Körper. ZAMM8, 85-106) model of plasticity. Such transitions are assumed to take place on a characteristic time scale T, with a nonlinear viscous response that becomes a plastic response for T→0 . We consider both discrete mechanical systems and their continuum mechanical analogues, showing how the Reiner-Rivlin fluid arises from nonlinear isotropic elasticity. A brief discussion is given in the conclusions of the possible extensions to other dissipative processes.
We propose and validate a three-dimensional continuum modeling approach that predicts small-amplitude acoustic behavior of dense-packed granular media. The model is obtained through a joint experimental and finite-element study focused on the benchmark example of a vibrated container of grains. Using a three-parameter linear viscoelastic constitutive relation, our continuum model is shown to quantitatively predict the effective mass spectra in this geometry, even as geometric parameters for the environment are varied. Further, the model's predictions for the surface displacement field are validated mode-by-mode against experiment. A primary observation is the importance of the boundary condition between grains and the quasirigid walls.
Dense granular materials display a complicated set of flow properties, which differentiate them from ordinary fluids. Despite their ubiquity, no model has been developed that captures or predicts the complexities of granular flow, posing an obstacle in industrial and geophysical applications. Here we propose a 3D constitutive model for well-developed, dense granular flows aimed at filling this need. The key ingredient of the theory is a grain-size-dependent nonlocal rheology—inspired by efforts for emulsions—in which flow at a point is affected by the local stress as well as the flow in neighboring material. The microscopic physical basis for this approach borrows from recent principles in soft glassy rheology. The size-dependence is captured using a single material parameter, and the resulting model is able to quantitatively describe dense granular flows in an array of different geometries. Of particular importance, it passes the stringent test of capturing all aspects of the highly nontrivial flows observed in split-bottom cells—a geometry that has resisted modeling efforts for nearly a decade. A key benefit of the model is its simple-to-implement and highly predictive final form, as needed for many real-world applications.
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